GMAT Math : Arithmetic

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Example Questions

Example Question #32 : Understanding Fractions

$\frac{3}{8}$ of a number, , is . What is ?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem by setting up our equation and solving for the number, :

$\frac{3}{8}n=24$

3n=(8)(24)

3n=192

n=64

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Example Question #33 : Understanding Fractions

$\frac{5}{16}$ of a number, , is 125 . What is the value of ?

Possible Answers:

$39 \frac{1}{6}$

625

400

200

Correct answer:

400

Explanation:

$\frac{5}{16}n=125$

5n=(125)(16)

5n=2000

n=400

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Example Question #32 : Understanding Fractions

Solve:

$\frac{3}{8} + \frac{2}{9} =$

Possible Answers:

$\frac{5}{17}$

$\frac{5}{8}$

$\frac{6}{72}$

$\frac{5}{9}$

$\frac{43}{72}$

Correct answer:

$\frac{43}{72}$

Explanation:

In order to add the two fractions, we must find the lowest common denominator. To do this, we simply multiply each fraction by the denominator of the opposite over itself:

$\frac{9}{9}\cdot\frac{3}{8} + \frac{8}{8}\cdot \frac{2}{9} = \frac{27}{72} + \frac{16}{72} = \frac{43}{72}$

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Example Question #392 : Arithmetic

Simplify the following into a single fraction.

$\frac{a}{b} + \frac{6a}{7c}$

Possible Answers:

$\frac{7a}{7c+b}$

None of the other answers.

$\frac{a}{7bc}$

$\frac{a}{bc}$

$\frac{a(7c+6b)}{7bc}$

Correct answer:

$\frac{a(7c+6b)}{7bc}$

Explanation:

To simply, we must first find the common denominator of the two fractions. That would be $b \times 7c$ or 7bc

Hence we multiply the first fraction by $\frac{7c}{7c}$ and the second fraction by $\frac{b}{b}$ , and we will have.

$\frac{7ac}{7bc} + \frac{6ab}{7bc}$ .

Now that the denominators match, we can add the fractions. The denominator stays the same after this, only the numerators add together.

$\frac{7ac+6ab}{7bc}$

Then factor out an from the numerator to get the final answer.

$\frac{a(7c+6b)}{7bc}$

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Example Question #1 : Understanding Decimals

Rewrite as a fraction in lowest terms: $0.7\overline{5}$

Possible Answers:

$\frac{3}{4}$

$\frac{8}{11}$

$\frac{34}{45}$

$\frac{74}{99}$

$\frac{25}{33}$

Correct answer:

$\frac{34}{45}$

Explanation:

$N = 0.7\overline{5} = 0.7555...$

100N = 75.55...

$\underline{10N }=\; \underline{ 7.555...}$

90N = 68

$N = \frac{68}{90} = \frac{68 \div 2}{90\div 2} = \frac{34}{45}$

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Example Question #1 : Understanding Decimals

Add one hundred seven ten-thousandths to seventeeen one-hundredths.

Possible Answers:

One thousand seven hundred seventeen ten-thousandths

One thousand one hundred seventy-seven ten-thousandths

Two hundred seventy-seven one-thousandths

One hundred eighty-seven one-thousandths

One thousand eight hundred seven ten-thousandths

Correct answer:

One thousand eight hundred seven ten-thousandths

Explanation:

One hundred seven ten-thousandths = 0.0107

Seventeeen one-hundredths = 0.17, or 0.1700

The sum:

$\begin{matrix} \; \; \; 0.1700\\ + \underline{0.0107} \\ \; \; \; 0.1807\end{matrix}$

This is one thousand eight hundred seven ten-thousandths.

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Example Question #1 : Understanding Decimals

Multiply seventy-seven one-hundredths by sixty-six one-thousandths.

Possible Answers:

Forty-six thousand six hundred sixty-two hundred-thousandths

Five thousand eighty-two ten-thousandths

Five thousand eighty-two hundred-thousandths

Five hundred eighty-two ten-thousandths

Five hundred eighty-two hundred-thousandths

Correct answer:

Five thousand eighty-two hundred-thousandths

Explanation:

Seventy-seven one-hundredths = 0.77

Sixty-six one-thousandths = 0.066

The product:

$\begin{matrix} \;\; 0.77\\ \; \underline{0.066} \; \end{matrix}$

$\rightarrow$ $\begin{matrix} \; \; \; \; \; 77\\ \; \; \; \; \; \underline{66}\\ \; \; \; 462\\ \underline{462\; }\\ 5082 \end{matrix}$

0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right.

$0.77 \times 0.066 = 0.05082$

This is five thousand eighty-two hundred-thousandths.

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Example Question #1 : Understanding Decimals

Divide eight hundred eighty-eight thousandths by sixty-four ten-thousandths.

Possible Answers:

12.6375

138.75

126.375

13.875

1,263.75

Correct answer:

138.75

Explanation:

Eight hundred eighty-eight thousandths = 0.888

Sixty-four ten-thousandths = 0.0064

Set up a long division:

Division

Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.

Division

(Note that leading zeroes have been removed.)

Carry out the long division, making sure you align the decimals:

Division

The quotient of this division is that of the original problem, so the correct choice is 138.75.

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Example Question #2 : Understanding Decimals

Which of the following is the square of twenty seven one-thousandths?

Possible Answers:

The correct answer is not among the other responses.

Fifty-four one-millionths

Seven hundred twenty-nine one-hundred-thousandths

Fifty-four one-hundred-thousandths

Seven hundred twenty-nine one-millionths

Correct answer:

Seven hundred twenty-nine one-millionths

Explanation:

Twenty-seven one-thousandths = 0.027

Its square is

$0.027^{2} = 0.027 \times 0.027$

Multiply without regard to the decimals first:

$27 \times 27 = 729$

0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

$0.027 \times 0.027= 0.000729$

This is seven hundred twenty-nine one-millionths.

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Example Question #3 : Understanding Decimals

Which of the following is the cube of fifteen one-hundredths?

Possible Answers:

Three thousand three hundred seventy-five one-hundred-thousandths

Three thousand three hundred seventy-five one-millionths

Forty-five one-millionths

The correct answer is not among the other responses.

Forty-five one-hundred-thousandths

Correct answer:

Three thousand three hundred seventy-five one-millionths

Explanation:

Fifteen one-hundredths = 0.15

Its cube is $0.15 ^{3} =0.15 \times 0.15 \times 0.15$

Multiply without regard to the decimals first:

$15 \times 15 \times 15 = 3,375$

0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

$0.15 \times 0.15 \times 0.15= 0.003375$

This is three thousand three hundred seventy-five one-millionths.

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #32 : Understanding Fractions

Example Question #33 : Understanding Fractions

Example Question #32 : Understanding Fractions

Example Question #392 : Arithmetic

Example Question #1 : Understanding Decimals

Example Question #1 : Understanding Decimals

Example Question #1 : Understanding Decimals

Example Question #1 : Understanding Decimals

Example Question #2 : Understanding Decimals

Example Question #3 : Understanding Decimals

All GMAT Math Resources

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